Practice Ordered Pair Solutions to Linear Equations

To check whether an ordered pair (a, b) is a solution of an equation, substitute these values into the equation and determine if the resulting equality is true or false.

To check whether (2, 11) is a solution of the equation, let's substitute ‍\(x=2\) and \(y=11\) into the equation:

\(\begin{aligned}{y}&=3{x}+5\\
{11}&=3\cdot{2}+5\\
11&=6+5\\
11&=11\end{aligned}\)

Since \(11=11\), we obtained a true statement, so (2,11) is indeed a solution of the equation.

To check whether (3, 13) is a solution of the equation, let's substitute ‍\(x=3\) and \(y=13\) into the equation:

\(\begin{aligned}{y}&=3{x}+5\\
{13}&=3\cdot{3}+5\\
13&=9+5\\
13&=14\end{aligned}\)

Since \(13 \neq 14\), we obtained a false statement, so (3, 13) is not a solution of the equation.

Only (2,11) is a solution of the equation.

To check whether an ordered pair (a, b) is a solution of an equation, substitute these values into the equation and determine if the resulting equality is true or false.

To check whether (4, -1) is a solution of the equation, let's substitute ‍\(x=4\) and \(y=-1\) into the equation:

\(\begin{aligned}{y}+1&=3({x}-4)\\
{-1}+1&=3({4}-4)\\
0&=3\cdot 0\\
0&=0\end{aligned}\)

Since \(0=0\), we obtained a true statement, so (4, -1) is indeed a solution of the equation.

To check whether (5, 2) is a solution of the equation, let's substitute ‍\(x=5\) and \(y=2\) into the equation:

\(\begin{aligned}{y}+1&=3({x}-4)\\
{2}+1&=3({5}-4)\\
3&=3\cdot 1\\
3&=3\end{aligned}\)

Since \(3=3\), we obtained a true statement, so (5, 2) is indeed a solution of the equation.

Both ordered pairs are solutions of the equation.

To check whether an ordered pair (a, b) is a solution of an equation, substitute these values into the equation and determine if the resulting equality is true or false.

To check whether (3, 15) is a solution of the equation, let's substitute ‍\(x=3\) and \(y=15\) into the equation:

\(\begin{aligned}{y}&=7{x}-2\\
{15}&=7\cdot {3}-2\\
15&=21-2\\
15&=19\end{aligned}\)

Since \(15 \neq 19\), we obtained a false statement, so (3, 15) is not a solution of the equation.

To check whether (-1, 10) is a solution of the equation, let's substitute ‍\(x=-1\) and \(y=-10\) into the equation:

\(\begin{aligned}{y}&=7{x}-2\\
{-10}&=7\cdot({-1})-2\\
-10&=-7-2\\
-10&=-9\end{aligned}\)

Since \(-10 \neq -9\), we obtained a false statement, so (-1, -10) is not a solution of the equation.

Neither of the ordered pairs is a solution of the equation.

To check whether an ordered pair (a, b) is a solution of an equation, substitute these values into the equation and determine if the resulting equality is true or false.

To check whether (2, 4) is a solution of the equation, let's substitute ‍\(x=2\) and \(y=4\) into the equation:

\(\begin{aligned}-3{x}+5{y}&=2{x}+3{y}\\
-3\cdot{2}+5\cdot{4}&=2\cdot{2}+3\cdot{4}\\
-6+20&=4+12\\
14&=16\end{aligned}\)

Since \(14 \neq 16\), we obtained a false statement, so (2, 4) is not a solution of the equation.

To check whether (3, 3) is a solution of the equation, let's substitute ‍\(x=3\) and \(y=3\) into the equation:

\(\begin{aligned}-3{x}+5{y}&=2{x}+3{y}\\
-3\cdot{3}+5\cdot{3}&=2\cdot{3}+3\cdot{3}\\
-9+15&=6+9\\
6&=15\end{aligned}\)

Since \(6 \neq 15\), we obtained a false statement, so (3, 3) is not a solution of the equation.

Neither of the ordered pairs is a solution of the equation.